Not knobs

The first five chapters discussed four kinds of signal: dopamine and reward prediction, cortisol and the stress response, testosterone and social challenge, serotonin and light with the rhythm of mood, plus autonomic balance. Popular accounts often treat them as knobs that can each be set to a “best value”: dopamine high, cortisol low, testosterone high, serotonin high. The idea has two problems.

First, they are not quantities that can be set independently. They sit in coupled loops: cortisol inhibits the gonadal axis (Chapter 3), light shifts the circadian clock, which in turn sets the daily rhythm of cortisol (Chapter 4), and the average reward rate sets the vigour of action (Chapter 1). Change one and the others change too.

Second, even if they could be set independently, no single value would be best for every goal. An acute rise in cortisol helps to meet an immediate challenge and works against long-term repair; the drive to pursue new rewards helps exploration and works against rest. This is a multi-objective problem.

The Pareto front of a schedule

# Toy model: there is no single best "state", only trade-offs. A working day of 8 hours is split into
# blocks of effort and breaks. Fatigue F rises during effort and falls during rest; output per minute is
# (1 - F). Two objectives: total output (higher is better) and mean fatigue over the day (lower is better).
# A schedule is on the Pareto front if no other schedule is better on one objective and no worse on the other.
def day(block, brk, minutes=480, a=0.006, b=0.04):
    F, out, t, load = 0.0, 0.0, 0, 0.0
    while t < minutes:
        for _ in range(block):
            if t >= minutes: break
            out += 1 - F; F += a * (1 - F); t += 1; load += F
        for _ in range(brk):
            if t >= minutes: break
            F -= b * F; t += 1; load += F
    return out, load / minutes

options = [(blk, brk) for blk in (25, 45, 60, 90, 120, 240, 480) for brk in (0, 5, 10, 15, 20, 30)
           if not (brk == 0 and blk != 480)]
res = {o: day(*o) for o in options}
front = [o for o in options if not any(res[p][0] >= res[o][0] and res[p][1] <= res[o][1] and res[p] != res[o]
                                       for p in options)]
print("effort block / break (min)   output   mean fatigue")
for o in sorted(front, key=lambda o: res[o][0]):
    print(f"{o[0]:5d} / {o[1]:2d}                  {res[o][0]:6.0f}   {res[o][1]:5.2f}")
print(f"{len(front)} of {len(options)} schedules are on the front; none is best on both objectives.")
print(f"no breaks at all: output {res[(480, 0)][0]:.0f}, fatigue {res[(480, 0)][1]:.2f}")
# effort block / break (min)   output   mean fatigue
#    25 / 30                     200    0.11
#    25 / 20                     234    0.15
#    45 / 30                     246    0.18
#    25 / 15                     246    0.18
#    60 / 30                     256    0.22
#    45 / 20                     262    0.23
#    25 / 10                     267    0.24
# 7 of 36 schedules are on the front; none is best on both objectives.
# no breaks at all: output 157, fatigue 0.67

The model’s conclusion does not depend on the particular parameters: as long as fatigue accumulates and rest lets it recover, there is no single optimal schedule, only a set of schedules that are best under some trade-off. Which to choose depends on what you value more. With these parameters, working without any break gives neither the highest output nor the lowest fatigue; but specific conclusions such as “25 minutes of work and 10 of rest is best” come entirely from assumed parameters and should not be taken as advice.

Rhythms of alternation

When several goals conflict, a common biological solution is not to find a fixed compromise but to alternate in time: favour one goal for a while, then another. The circadian rhythm is the clearest example: by day cortisol and sympathetic activity are higher, which suits action; at night melatonin rises and parasympathetic activity is higher, which suits repair.

Summary

There is no state in which every hormone sits at a “best value”. What can really be arranged is the rhythm by which different goals take turns over a day and a week: action alternating with repair, and challenges given a clear end. The next chapter turns to how ancient writers thought about the same question.